This is probably the most popular choice of frequency. The theta state is a state of tremendous stress relief. The benefits associated with theta level relaxation include improved concentration, reduced hyperactivity and improved memory. While in a state of theta relaxation, one’s blood pressure, breathing and heart rate all slow to a much more restful and healthy level that promotes natural healing. During theta relaxation one may also experience vivid flashes of mental imagery as the mind opens to memories or subconscious information that is not available to the conscious mind during the normal waking state. The theta state is a very deep state of relaxation that is excellent for deep hypnosis and mental programming.

The huge problem will all such studies is that there is a clear placebo effect on any kind of mental performance whenever the subject is observed. Do any intervention, then measure performance, and the intervention and measurement are likely to cause an increase in effort and attention which will increase performance. This generic “placebo” effect needs to be factored out of any such study by proper blinding and controls in order for the results to have any meaning at all.
So to summarize their claim, they're saying that entrainment means that a binaural beat will cause your brain's electroencephalogram to match the pattern of the phantom beat. Well, if it did, entrainment certainly doesn't apply and would not be part of the equation, so we can scratch that off the list. But it doesn't make the claimed observation wrong. We do know that certain electroencephalogram waveforms are often associated with certain kinds of activity. For example, physical activity or REM sleep often produces an electroencephalogram with a sine wave of between 4 and 8 Hz, which we term a theta pattern. Waking relaxation with eyes closed often produces a pattern from 8 to 12 Hz, which is called an alpha pattern. There are only a few characterized patterns, and pretty general descriptions of what kinds of activities go with them. The claim made by the binaural beat sellers depends on much more granular and specific matches. For example, the claim that a binaural beat with a frequency of X produces the same effect in your brain as Vicodin is wholly implausible. Such claims presume that we know the exact frequency of the electroencephalogram in each of these desired conditions, and the fact is that brain waves don't work that way. It is wholly and absolutely implausible to say that desired brain condition X will occur if we get your EEG to read exactly X Hz.
Despite the vast differences between each individual, our brain’s inner workings are remarkably similar. Brainwave Entrainment was built around these fundamental similarities and has equally powerful effects for almost everyone who uses it. While each situation may require a different frequency or audio track, Brainwave Love has one of the most complete, effective libraries to cover your every need. Take a look now:
Many people exercise to control weight and get in better physical condition to become more healthy or physically attractive, but exercise and stress management are also closely linked. Exercise provides a distraction from stressful situations, as well as an outlet for frustrations, and gives you a lift via endorphins as well. This article can tell you more about the stress management benefits of exercise, and help you get more active in your daily life.
Above is a nice, simple and short chart of the various brainwave ranges and the types of effects they generally have and what sorts of activities they may be able to enhance. There simply is nothing more detailed than what this chart contains about entrainment frequencies and what they are useful for. Those other elaborate lists to be found on the internet are nothing but the product of overactive imaginations.

SPEAKER: You know those people who always seem to be smiling? What's their secret? Turns out a lot of the smiles come from saying sayonara stress. Want in on that action? Well, here are three ways to stress less so you can smile more. First up, play your stress away/ why should kids have all the fun? Your boss might not let everyone out for recess, but you can find 15 minutes every day to do something you really enjoy. Go to a driving range. Play ping pong, cards, or board games. Just keep it friendly. Remember, winning isn't everything. Number 2. Give it up for pet power. Have you ever seen anyone looking stressed when playing with an adorable puppy? Neither have we. Interacting with animals has been proven to lower stress in almost everyone. Simply petting a dog or a cat lowers your blood pressure considerably and reduces levels of the stress-causing hormone cortisol. So pet your pooch. Don't have a pet? Borrow a friend's, or visit a local shelter for some much-needed cuddle time. And the number-one way to stress less? Laugh it off. How does laughter love thee? Let us count the ways. Laughter fills your body and lungs with oxygen. It makes your brain release Mr. And Mrs. Happy Hormones, the endorphins. It bolsters your immune system and helps you, well, be well. It also helps your brain release natural pain relievers, and may even stop painful muscle spasms. It's true. He who laughs best stresses less. So learn to play, adopt a stray, and laugh away. You'll feel great. And it will show.

Why is exposure to these soundwaves helpful to sleep and relaxation? Science shows that exposure to binaural beats can create changes in the brain’s degree of arousal. Listening to these sounds that create a low-frequency tone, research indicates, triggers a slow-down to brainwave activity—and that may help you relax, lower your anxiety, and can make it easier for you to fall asleep and sleep more soundly.
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When stress overwhelms your nervous system, your body is flooded with chemicals that prepare you for “fight or flight.” This stress response can be lifesaving in emergency situations where you need to act quickly. But when it’s constantly activated by the stresses of everyday life, it can wear your body down and take a toll on your emotional and physical health.

Beta brainwaves are further divided into three bands; Lo-Beta (Beta1, 12-15Hz) can be thought of as a 'fast idle', or musing. Beta (Beta2, 15-22Hz) is high engagement or actively figuring something out. Hi-Beta (Beta3, 22-38Hz) is highly complex thought, integrating new experiences, high anxiety, or excitement. Continual high frequency processing is not a very efficient way to run the brain, as it takes a tremendous amount of energy. 
Neural oscillations are rhythmic or repetitive electrochemical activity in the brain and central nervous system. Such oscillations can be characterized by their frequency, amplitude and phase. Neural tissue can generate oscillatory activity driven by mechanisms within individual neurons, as well as by interactions between them. They may also adjust frequency to synchronize with the periodic vibration of external acoustic or visual stimuli.[3]